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Abstract

Thermal modelling is of great importance in all electric machines but especially in permanent
magnet synchronous machines (PMSMs). The thermally fragile permanent magnets (PMs) can
more easily be demagnetized at high temperatures. When high speed machines are considered,
heat extraction surfaces are small due to the higher energy density. This thesis focuses on the
thermal modelling of a high speed slotless PMSM using analytical techniques. From literature
it is clear that analytical distributed models have not reached its full potential in thermal modelling
of electric machines. Thermal experiments on high speed electric machine, including
rotor PM temperature measurements are not commonly found in literature.
The thermal behaviour of each component of the machine is influenced by the overall temperature
distribution. The widely used lumped parameter (LP) cylindrical component model
derived by Mellor et al. is used to derive a LP model of the entire machine. A two dimensional
(2-D) analytical distributed model is derived for the rotor PM using the separation of variables
method. Three of the boundaries are assumed to be of the convection type and the fourth of
constant heat flow type. Different convection coefficients are assumed to exist in the radial and
axial directions. The distributed model is verified using COMSOL
R and good correlation is
shown. The distributed model is used to determine the temperature distribution in the PM
and the convection heat flow in the axial direction.
Loss calculation is an integral part of thermal modelling. Temperature changes in an electric
machine is due to the interaction between the heat generation (losses) and heat removal. The
losses found in a high speed slotless PMSM are investigated. A 2-D analytical magnetic model
is used to determine the stator lamination loss as well as the stator winding eddy current loss. A
simple LP model is derived for the rotor eddy current loss. Due to the relatively large resistivity
of the shielding cylinder and PM material, the rotor eddy current loss is a significant part of the
total machine loss. The tangential current width is determined empirically in this thesis but a
3-D distributed model which includes end space effects and skin depth could also be used.
A large part of thermal modelling is empirically based. The convection and interface resistances
are determined through a set of experiments in this thesis. The measured and calculated
convection coefficients correlated well for both forced and natural convection cooling. A large
temperature increase found during the no-load test can be attributed to large bearing loss, possibly
due to axial loading. The LP model is modified to include the phenomena found during
the experiments.
The thermal model is used to predict the temperatures of a high speed PMSM at rated load and speed. Although the PM is not heated above the Curie temperature, demagnetization is
still possible. According to the model, the machine will not be able to operate at full load and
speed for extensive periods due to mechanical stress limits being exceeded. The temperature
distribution of the PM could not be verified since the temperatures in the air gap and end space
could not be measured. It is expected that axial heat flow will be larger than what is currently
predicted by the distributed model. A sensitivity analysis was used to investigate the influence
of the thermal resistances and losses on the machine temperatures. Methods for reducing the
rotor eddy current loss and interface resistances are also discussed.
The first contribution of this thesis is the 2-D analytical distributed model for the PM of a high
speed PMSM. Hot spots and 2-D heat flow can be analysed using this model. Combining the
LP and 2-D analytical distributed models is another contribution. This combines the simplicity
and fast solution times of the LP model with the 2-D thermal distribution of the analytical
distributed model. The systematic experimental investigation of the thermal behaviour of a
high speed PMSM is a further contribution.